CN111069708A - Arc-shaped tooth machining process applied to speed reducer - Google Patents
Arc-shaped tooth machining process applied to speed reducer Download PDFInfo
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- CN111069708A CN111069708A CN201911384400.6A CN201911384400A CN111069708A CN 111069708 A CN111069708 A CN 111069708A CN 201911384400 A CN201911384400 A CN 201911384400A CN 111069708 A CN111069708 A CN 111069708A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F17/00—Special methods or machines for making gear teeth, not covered by the preceding groups
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F15/00—Methods or machines for making gear wheels of special kinds not covered by groups B23F7/00 - B23F13/00
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F17/00—Special methods or machines for making gear teeth, not covered by the preceding groups
- B23F17/006—Special methods or machines for making gear teeth, not covered by the preceding groups using different machines or machining operations
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23P—METAL-WORKING NOT OTHERWISE PROVIDED FOR; COMBINED OPERATIONS; UNIVERSAL MACHINE TOOLS
- B23P15/00—Making specific metal objects by operations not covered by a single other subclass or a group in this subclass
- B23P15/14—Making specific metal objects by operations not covered by a single other subclass or a group in this subclass gear parts, e.g. gear wheels
Abstract
The invention relates to an arc-shaped tooth processing technology applied to a speed reducer, which comprises the following steps: s1: firstly, reasonably selecting gear materials: the gear is made of alloy quenched and tempered steel; s2: forming a gear blank: forgings and castings; s3: rough machining of the gear: processing a gear blank, a gear shape and a gear end, and cutting off redundant materials; s4: semi-finishing the gear; polishing and deslagging the formed arc-shaped rack by using a shot blasting machine; s5: gear heat treatment: preheating, quenching and tempering; s6: secondary fine machining: putting the semi-finished gear into a gear grinding machine for secondary finish machining, and finishing the tooth profile to obtain a finished product; the preheating condition in S5 is 550-. The quenching condition is 800-. The tempering condition is 500-.
Description
Technical Field
The invention relates to the field of gears, in particular to an arc-shaped gear machining process applied to a speed reducer.
Background
With the development and progress of society, more and more manual works have been replaced to the processing of machinery finished product, because the rotational speed of motor is very fast, in order to reach required rotational speed in the actual use, the output shaft of motor need connect the reduction gear before can connect to next job order at first.
The existing speed reducer needs to be compact in space for saving equipment or devices, but the strength requirement of the gear of the speed reducer is very high, the gear in the speed reducer needs to be meshed for a long time, damage can occur, and the normal operation of the speed reducer is influenced.
The invention provides an arc-shaped tooth processing technology applied to a speed reducer, which can improve the strength of gear teeth.
Disclosure of Invention
The invention provides an arc-shaped tooth processing technology applied to a speed reducer, aiming at solving the problems in the prior art, and the processing technology comprises the following steps:
s1: firstly, reasonably selecting gear materials: the gear is made of alloy quenched and tempered steel;
s2: forming a gear blank: forgings and castings;
s3: rough machining of the gear: processing a gear blank, a gear shape and a gear end, and cutting off redundant materials;
s4: semi-finishing the gear; polishing and deslagging the formed arc-shaped rack by using a shot blasting machine;
s5: gear heat treatment: preheating, quenching and tempering;
s6: secondary fine machining: putting the semi-finished gear into a gear grinding machine for secondary finish machining, and finishing the tooth profile to obtain a finished product;
the preheating condition in S5 is 550-. The quenching condition is 800-.
The tempering condition is 500-;
in S1, the alloy quenched and tempered steel comprises the following components in percentage by weight: c: 0.25 to 0.3%, Si: 0.3-0.45%, Mn: 0.80-1.15%, Cr: 1.20-2.5%, P: 0.015-0.018%, Al: 0.05-0.07%, Ni: 0.8 to 1.25%, Mo: 0.3-0.35%, Be: 0.05 to 0.07%, Ta: 0.015-0.018%, Zr: 0.3-0.35%, W: 0.08-0.15%, Nb: 0.08 to 0.15% and the balance of Fe and inevitable impurities.
On the basis of the above scheme and as a preferable scheme of the scheme: ratio C in AS1 described above: 0.25 to 0.3%, Si: 0.3%, Mn: 0.80%, Cr: 1.20%, P: 0.015%, Al: 0.05-0.07%, Ni: 0.8%, Mo: 0.3%, Be: 0.07%, Ta: 0.018%, Zr: 0.35%, W: 0.15%, Nb: 0.08%, and the balance of Fe and inevitable impurities.
On the basis of the above scheme and as a preferable scheme of the scheme: in the above-described rough machining of the gear in S3, a generating method machining method is used.
On the basis of the scheme, as a preferable scheme of the scheme, when the gear grinding machine is carried out, the inner diameter of a grinding disc is Ri, the outer diameter of the grinding disc is Ro, the center of the circle is O, the radius of a central circle of a grinding area is (Ri + Ro)/2, OB is a vertical bisector of the grinding area, the central circle of the grinding area is intersected with OB at a point B, if the arc-shaped tooth is in left-hand rotation, BE is conducted on the upper left side of OB after B is conducted, if the arc-shaped tooth is in right-hand rotation, BE is conducted on the upper right side of OB after B is conducted, the included angle between BE;
optionally selecting a point A on the circle in the grinding area, passing through A, B two points and making a circle by taking BE as a tangent line, wherein a straight line vertical to the tangent line BE and a straight line vertical to AD are intersected at a point O1Point of, O1I.e. the center of the circle passing through point A, B and tangent to BE and AD, the circle O is measured1The radius is Ra;
circle O1The intersection part of the BE and the OB is the central line of the arc-shaped tooth, the included angle β between the BE and the OB is set as the inclination angle of the arc-shaped tooth, and the included angle α between the AD and the OA is set as the initial inclination angle of the arc-shaped tooth;
designing an arc equation of the center of the arc-shaped tooth;
selecting O1As the pole, a horizontal ray is led as the polar axis, the counterclockwise direction is taken as the positive direction, and the circle O is1The angle between the connecting line of any point and the pole axis is to obtain a circle O1The equation of (a) is:
formula (1) is a circular equation where the arc-shaped grinding tooth central arc line AC is located;
designing an internal and external arc equation of the grinding teeth;
if the tooth width of the arc-shaped tooth is b, the equations of the inner arc line and the outer arc line of the grinding tooth are respectively as follows:
and step four, distributing the number n of the arc-shaped grinding teeth according to the size of the grinding disc and the process requirement, and carrying out circumferential array on the established grinding tooth edge so as to finish the design of the radial arc-shaped tooth arc line.
Based on the scheme, as a preferable scheme of the scheme, one point A is selected as a grinding tooth starting point on the inner diameter of the grinding sheet, Ri is 150mm, Ro is 450mm, the radius of a central arc line of a grinding area is 300mm, β is 45 degrees, one point A is selected, BE is used as a tangent line to make a circle O1 for A, and BE is used as a tangent line to make a circle O1 for A1The tangent line AD, AD and OA include an included angle α of 43.16 degrees and α is the initial inclination angle of the grinding teeth measured by the circle O1Radius 205.4mm, circle O1The equation is:
considering the width of the grinding teeth, the internal and external arc line equations of the grinding teeth are respectively as follows:
and obtaining inner and outer arcs of grinding teeth, arranging 11 arc-shaped grinding teeth in the grinding disc, and performing circumferential array on the established grinding tooth edges.
Compared with the prior art, the invention has the outstanding and beneficial technical effects that:
1. the tooth surface of the invention forms an arc structure protruding outwards from the tooth root to the tooth top, so that the engaging surface of the gear is wider in the engaging process, and the contact stress between the tooth surfaces and the bending stress of the tooth root are reduced;
2. because the tooth surface is in an arc design, the additional impact force generated by the two gears which are in contact at the meshing point is small, and the meshing impact and the noise are reduced.
In conclusion, the arc-shaped teeth produced by the arc-shaped tooth production process can increase the hardness of the tooth surface, reduce the impact force of gear meshing, prolong the service life of the gear and prolong the service life of the speed reducer.
Detailed Description
The technical solution of the present invention is further illustrated by the following examples.
The first embodiment is as follows:
the conventional gear produced by the conventional gear production method has the tooth surface which is not arc-shaped.
Example two:
the invention relates to an arc-shaped tooth processing technology applied to a speed reducer, which comprises the following steps:
s1: firstly, reasonably selecting gear materials: the gear is made of alloy quenched and tempered steel;
s2: forming a gear blank: forgings and castings;
s3: rough machining of the gear: processing a gear blank, a gear shape and a gear end, and cutting off redundant materials;
s4: semi-finishing the gear; polishing and deslagging the formed arc-shaped rack by using a shot blasting machine;
s5: gear heat treatment: preheating, quenching and tempering;
s6: secondary fine machining: putting the semi-finished gear into a gear grinding machine for secondary finish machining, and finishing the tooth profile to obtain a finished product; the gear machined by the gear grinding has the advantages of low transmission noise, high transmission efficiency and long service life.
The preheating condition in S5 was 550 deg.C/40 min. The quenching condition is 850 ℃/90 min. The tempering condition is 500 ℃/3 h;
in S1, the alloy quenched and tempered steel comprises the following components in percentage by weight: c: 0.25 to 0.3%, Si: 0.3%, Mn: 0.80%, Cr: 1.20%, P: 0.015%, Al: 0.05-0.07%, Ni: 0.8%, Mo: 0.3%, Be: 0.07%, Ta: 0.018%, Zr: 0.35%, W: 0.15%, Nb: 0.08%, and the balance of Fe and inevitable impurities.
In the above-described rough machining of the gear in S3, a generating method machining method is used.
When the gear grinding machine is used, the inner diameter of a grinding disc is Ri, the outer diameter is Ro, the center of the circle is O, the radius of a central circle of a grinding area is (Ri + Ro)/2, OB is a vertical bisector of the grinding area, the central circle of the grinding area is intersected with OB at a point B, if the arc-shaped tooth is in a left-hand rotation, BE is processed on the upper left side of OB after B is processed, if the arc-shaped tooth is in a right-hand rotation, BE is processed on the upper right side of OB after B is processed, the included angle between BE and OB is;
optionally selecting a point A on the circle in the grinding area, passing through A, B two points and making a circle by taking BE as a tangent line, wherein a straight line vertical to the tangent line BE and a straight line vertical to AD are intersected at a point O1Point of, O1I.e. the center of the circle passing through point A, B and tangent to BE and AD, the circle O is measured1The radius is Ra;
circle O1The intersection part of the BE and the OB is the central line of the arc-shaped tooth, the included angle β between the BE and the OB is set as the inclination angle of the arc-shaped tooth, and the included angle α between the AD and the OA is set as the initial inclination angle of the arc-shaped tooth;
designing an arc equation of the center of the arc-shaped tooth;
selecting O1As the pole, a horizontal ray is led as the polar axis, the counterclockwise direction is taken as the positive direction, and the circle O is1The angle between the connecting line of any point and the pole axis is theta to obtain a circle O1The equation of (a) is:
formula (1) is a circular equation where the arc-shaped grinding tooth central arc line AC is located;
designing an internal and external arc equation of the grinding teeth;
if the tooth width of the arc-shaped tooth is b, the equations of the inner arc line and the outer arc line of the grinding tooth are respectively as follows:
and step four, distributing the number n of the arc-shaped grinding teeth according to the size of the grinding disc and the process requirement, and carrying out circumferential array on the established grinding tooth edge so as to finish the design of the radial arc-shaped tooth arc line.
Based on the scheme, as a preferable scheme of the scheme, one point A is selected as a grinding tooth starting point on the inner diameter of the grinding sheet, Ri is 150mm, Ro is 450mm, the radius of a central arc line of a grinding area is 300mm, β is 45 degrees, one point A is selected, BE is used as a tangent line to make a circle O1 for A, and BE is used as a tangent line to make a circle O1 for A1The tangent line AD, AD and OA include an included angle α of 43.16 degrees and α is the initial inclination angle of the grinding teeth measured by the circle O1Radius 205.4mm, circle O1The equation is:
considering the width of the grinding teeth, the internal and external arc line equations of the grinding teeth are respectively as follows:
and obtaining inner and outer arcs of grinding teeth, arranging 11 arc-shaped grinding teeth in the grinding disc, and performing circumferential array on the established grinding tooth edges.
Example three:
the invention relates to an arc-shaped tooth processing technology applied to a speed reducer, which comprises the following steps:
s1: firstly, reasonably selecting gear materials: the gear is made of alloy quenched and tempered steel;
s2: forming a gear blank: forgings and castings;
s3: rough machining of the gear: processing a gear blank, a gear shape and a gear end, and cutting off redundant materials;
s4: semi-finishing the gear; polishing and deslagging the formed arc-shaped rack by using a shot blasting machine;
s5: gear heat treatment: preheating, quenching and tempering;
s6: secondary fine machining: putting the semi-finished gear into a gear grinding machine for secondary finish machining, and finishing the tooth profile to obtain a finished product; the gear machined by the gear grinding has the advantages of low transmission noise, high transmission efficiency and long service life.
The preheating condition in S5 was 650 deg.C/40 min. The quenching condition is 800 ℃/90 min. The tempering condition is 600 ℃/4 h;
in S1, the alloy quenched and tempered steel comprises the following components in percentage by weight: c: 0.3%, Si: 0.45%, Mn: 0.80%, Cr: 2.5%, P: 0.018%, Al: 0.05%, Ni: 0.8%, Mo: 0.35%, Be: 0.05%, Ta: 0.015%, Zr: 0.35%, W: 0.08%, Nb: 0.08%, and the balance of Fe and inevitable impurities.
In the above-described rough machining of the gear in S3, a generating method machining method is used.
When the gear grinding machine is used, the inner diameter of a grinding disc is Ri, the outer diameter is Ro, the center of the circle is O, the radius of a central circle of a grinding area is (Ri + Ro)/2, OB is a vertical bisector of the grinding area, the central circle of the grinding area is intersected with OB at a point B, if the arc-shaped tooth is in a left-hand rotation, BE is processed on the upper left side of OB after B is processed, if the arc-shaped tooth is in a right-hand rotation, BE is processed on the upper right side of OB after B is processed, the included angle between BE and OB is;
optionally selecting a point A on the circle in the grinding area, passing through A, B two points and making a circle by taking BE as a tangent line, wherein a straight line vertical to the tangent line BE and a straight line vertical to AD are intersected at a point O1Point of, O1I.e. the center of the circle passing through point A, B and tangent to BE and AD, the circle O is measured1The radius is Ra;
circle O1The intersection part of the BE and the OB is the central line of the arc-shaped tooth, the included angle β between the BE and the OB is set as the inclination angle of the arc-shaped tooth, and the included angle α between the AD and the OA is set as the initial inclination angle of the arc-shaped tooth;
designing an arc equation of the center of the arc-shaped tooth;
selecting O1As the pole, a horizontal ray is led as the polar axis, the counterclockwise direction is taken as the positive direction, and the circle O is1The angle between the connecting line of any point and the pole axis is theta to obtain a circle O1The equation of (a) is:
formula (1) is a circular equation where the arc-shaped grinding tooth central arc line AC is located;
designing an internal and external arc equation of the grinding teeth;
if the tooth width of the arc-shaped tooth is b, the equations of the inner arc line and the outer arc line of the grinding tooth are respectively as follows:
and step four, distributing the number n of the arc-shaped grinding teeth according to the size of the grinding disc and the process requirement, and carrying out circumferential array on the established grinding tooth edge so as to finish the design of the radial arc-shaped tooth arc line.
Based on the scheme, as a preferable scheme of the scheme, one point A is selected as a grinding tooth starting point on the inner diameter of the grinding sheet, Ri is 150mm, Ro is 450mm, the radius of a central arc line of a grinding area is 300mm, β is 45 degrees, one point A is selected, BE is used as a tangent line to make a circle O1 for A, and BE is used as a tangent line to make a circle O1 for A1The tangent line AD, AD and OA include an included angle α of 43.16 degrees and α is the initial inclination angle of the grinding teeth measured by the circle O1Radius 205.4mm, circle O1The equation is:
considering the width of the grinding teeth, the internal and external arc line equations of the grinding teeth are respectively as follows:
and obtaining inner and outer arcs of grinding teeth, arranging 11 arc-shaped grinding teeth in the grinding disc, and performing circumferential array on the established grinding tooth edges.
Example four:
the invention relates to an arc-shaped tooth processing technology applied to a speed reducer, which comprises the following steps:
s1: firstly, reasonably selecting gear materials: the gear is made of alloy quenched and tempered steel;
s2: forming a gear blank: forgings and castings;
s3: rough machining of the gear: processing a gear blank, a gear shape and a gear end, and cutting off redundant materials;
s4: semi-finishing the gear; polishing and deslagging the formed arc-shaped rack by using a shot blasting machine;
s5: gear heat treatment: preheating, quenching and tempering;
s6: secondary fine machining: putting the semi-finished gear into a gear grinding machine for secondary finish machining, and finishing the tooth profile to obtain a finished product; the gear machined by the gear grinding has the advantages of low transmission noise, high transmission efficiency and long service life.
The preheating condition in S5 is 600 deg.C/40 min. The quenching condition is 820 ℃/90 min. The tempering condition is 550 ℃/3.5 h;
in S1, the alloy quenched and tempered steel comprises the following components in percentage by weight: c: 0.28%, Si: 0.35%, Mn: 0.85%, Cr: 1.25%, P: 0.015%, Al: 0.07%, Ni: 1.25%, Mo: 0.3%, Be: 0.06%, Ta: 0.018%, Zr: 0.35%, W: 0.1%, Nb: 0.12%, and the balance of Fe and inevitable impurities.
In the above-described rough machining of the gear in S3, a generating method machining method is used.
When the gear grinding machine is used, the inner diameter of a grinding disc is Ri, the outer diameter is Ro, the center of the circle is O, the radius of a central circle of a grinding area is (Ri + Ro)/2, OB is a vertical bisector of the grinding area, the central circle of the grinding area is intersected with OB at a point B, if the arc-shaped tooth is in a left-hand rotation, BE is processed on the upper left side of OB after B is processed, if the arc-shaped tooth is in a right-hand rotation, BE is processed on the upper right side of OB after B is processed, the included angle between BE and OB is;
optionally selecting a point A on the circle in the grinding area, passing through A, B two points and making a circle by taking BE as a tangent line, wherein a straight line vertical to the tangent line BE and a straight line vertical to AD are intersected at a point O1Point of, O1I.e. the center of the circle passing through point A, B and tangent to BE and AD, the circle O is measured1The radius is Ra;
circle O1The intersection part of the BE and the OB is the central line of the arc-shaped tooth, the included angle β between the BE and the OB is set as the inclination angle of the arc-shaped tooth, and the included angle α between the AD and the OA is set as the initial inclination angle of the arc-shaped tooth;
designing an arc equation of the center of the arc-shaped tooth;
selecting O1As the pole, a horizontal ray is led as the polar axis, the counterclockwise direction is taken as the positive direction, and the circle O is1The angle between the connecting line of any point and the pole axis is theta to obtain a circle O1The equation of (a) is:
formula (1) is a circular equation where the arc-shaped grinding tooth central arc line AC is located;
designing an internal and external arc equation of the grinding teeth;
if the tooth width of the arc-shaped tooth is b, the equations of the inner arc line and the outer arc line of the grinding tooth are respectively as follows:
and step four, distributing the number n of the arc-shaped grinding teeth according to the size of the grinding disc and the process requirement, and carrying out circumferential array on the established grinding tooth edge so as to finish the design of the radial arc-shaped tooth arc line.
Based on the scheme, as a preferable scheme of the scheme, one point A is selected as a grinding tooth starting point on the inner diameter of the grinding sheet, Ri is 150mm, Ro is 450mm, the radius of a central arc line of a grinding area is 300mm, β is 45 degrees, one point A is selected, BE is used as a tangent line to make a circle O1 for A, and BE is used as a tangent line to make a circle O1 for A1The tangent line AD, AD and OA include an included angle α of 43.16 degrees and α is the initial inclination angle of the grinding teeth measured by the circle O1Radius 205.4mm, circle O1The equation is:
considering the width of the grinding teeth, the internal and external arc line equations of the grinding teeth are respectively as follows:
and obtaining inner and outer arcs of grinding teeth, arranging 11 arc-shaped grinding teeth in the grinding disc, and performing circumferential array on the established grinding tooth edges.
The gears produced by the four embodiments have the following relevant detection data:
example one | Example two | EXAMPLE III | Example four | |
Tooth surface Hardness (HRC) | 55 | 73 | 76 | 70 |
Core Hardness (HRC) | 40 | 52 | 55 | 50 |
Tensile strength (Mpa) | 930.6 | 1309.5 | 1401.4 | 1289.7 |
Yield strength (Mpa) | 861.4 | 1092.8 | 1103.5 | 1022.4 |
Ultimate bending fatigue (Mpa) | 499.3 | 599.7 | 589.8 | 587.9 |
The invention has the advantages that:
the arc-shaped teeth produced by the arc-shaped tooth production process can increase the hardness of the tooth surface, reduce the impact force of gear meshing, prolong the service life of the gear and prolong the service life of the speed reducer.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (5)
1. The arc-shaped tooth processing technology applied to the speed reducer is characterized by comprising the following steps of:
s1: firstly, reasonably selecting gear materials: the gear is made of alloy quenched and tempered steel;
s2: forming a gear blank: forgings and castings;
s3: rough machining of the gear: processing a gear blank, a gear shape and a gear end, and cutting off redundant materials;
s4: semi-finishing the gear; polishing and deslagging the formed arc-shaped rack by using a shot blasting machine;
s5: gear heat treatment: preheating, quenching and tempering;
s6: secondary fine machining: putting the semi-finished gear into a gear grinding machine for secondary finish machining, and finishing the tooth profile to obtain a finished product;
the preheating condition in S5 is 550-. The quenching condition is 800-. The tempering condition is 500-;
in S1, the alloy quenched and tempered steel comprises the following components in percentage by weight: c: 0.25 to 0.3%, Si: 0.3-0.45%, Mn: 0.80-1.15%, Cr: 1.20-2.5%, P: 0.015-0.018%, Al: 0.05-0.07%, Ni: 0.8 to 1.25%, Mo: 0.3-0.35%, Be: 0.05 to 0.07%, Ta: 0.015-0.018%, Zr: 0.3-0.35%, W: 0.08-0.15%, Nb: 0.08 to 0.15% and the balance of Fe and inevitable impurities.
2. An arc-shaped tooth processing technology applied to a speed reducer according to claim 1, wherein the ratio C in the AS1 is AS follows: 0.25 to 0.3%, Si: 0.3%, Mn: 0.80%, Cr: 1.20%, P: 0.015%, Al: 0.05-0.07%, Ni: 0.8%, Mo: 0.3%, Be: 0.07%, Ta: 0.018%, Zr: 0.35%, W: 0.15%, Nb: 0.08%, and the balance of Fe and inevitable impurities.
3. The process of claim 2, wherein the rough machining of the gear in S3 is performed by generating method.
4. The process for machining the arc-shaped tooth applied to the speed reducer according to claim 1, wherein the gear grinding machine is used for grinding the tooth with the inner diameter of a grinding disc Ri, the outer diameter of the grinding disc Ro, the center of a circle of O, the central radius of a grinding area is (Ri + Ro)/2, OB is a vertical bisector of the grinding area, the central circle of the grinding area intersects OB at a point B, if the arc-shaped tooth is in a left-handed mode, BE is conducted on the upper left side of OB after B is passed, if the arc-shaped tooth is in a right-handed mode, BE is conducted on the upper right side of OB after B is passed, an included angle between BE and OB is;
optionally selecting a point A on the circle in the grinding area, passing through A, B two points and making a circle by taking BE as a tangent line, wherein a straight line vertical to the tangent line BE and a straight line vertical to AD are intersected at a point O1Point of, O1I.e. the center of the circle passing through point A, B and tangent to BE and AD, the circle O is measured1The radius is Ra;
circle O1The intersection part of the BE and the OB is the central line of the arc-shaped tooth, the included angle β between the BE and the OB is set as the inclination angle of the arc-shaped tooth, and the included angle α between the AD and the OA is set as the initial inclination angle of the arc-shaped tooth;
designing an arc equation of the center of the arc-shaped tooth;
selecting O1As the pole, a horizontal ray is led as the polar axis, the counterclockwise direction is taken as the positive direction, and the circle O is1The angle between the connecting line of any point and the pole axis is theta to obtain a circle O1The equation of (a) is:
formula (1) is a circular equation where the arc-shaped grinding tooth central arc line AC is located;
designing an internal and external arc equation of the grinding teeth;
if the tooth width of the arc-shaped tooth is b, the equations of the inner arc line and the outer arc line of the grinding tooth are respectively as follows:
and step four, distributing the number n of the arc-shaped grinding teeth according to the size of the grinding disc and the process requirement, and carrying out circumferential array on the established grinding tooth edge so as to finish the design of the radial arc-shaped tooth arc line.
5. The process for machining an arc-shaped tooth applied to a speed reducer according to claim 4, wherein a point A is selected as a tooth grinding starting point at the inner diameter of the grinding disc, Ri is 150mm, Ro is 450mm, the radius of a central arc line of a grinding area is 300mm, β is 45 degrees, a point A is selected, BE is used as a tangent line of the point A to form a circle O1, and the BE is used as a tangent line of the point A to form a circle O1The tangent line AD, AD and OA include an included angle α of 43.16 degrees and α is the initial inclination angle of the grinding teeth measured by the circle O1Radius 205.4mm, circle O according to polar coordinates as shown in FIG. 11The equation is:
considering the width of the grinding teeth, the internal and external arc line equations of the grinding teeth are respectively as follows:
and obtaining inner and outer arcs of grinding teeth, arranging 11 arc-shaped grinding teeth in the grinding disc, and performing circumferential array on the established grinding tooth edges.
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